I used núd once, for "number" but I think I was wrong. Parviphith has gwanod for it, (although I don't see why it has "gwa-" prefix,) and with Quenya's notë, I think it should simply be nod. We also have nedia- for counting, archaic nödia-.

Edit: I've found this at Eldamo, confirms nod :
http://eldamo.sourceforge.net/content/words/word-3743116979.html

Seeing this gave me an idea. How about pannod for "integer"? Plural pennyd. Integer in Turkish is "tam sayı" and it simply means "whole/complete/exact number".

+Ekin Gören Now I also think nod to be more probable; for some reason, I expected noth < not-te or not-se. Gonod- shouldn't be a noun at all, I think, if it's a verb 'to count up', then nod- is just 'to count'.
I very much like your idea of pannod; I wonder what numbers were known to the Eldar? Knowing their calendar, they were at ease with rational numbers, but there is, as I suspect, no evidence of the reals.

+Jenna Carpenter Not the word is improbable, but the meaning. Gwanod should be a sum, a total number, which renders the word useless for an abstract mathematical concept. I'd definitely use gwanod for 'a sum', but not 'a number'.